1. Let f(1/n) = n for positive integers n and f(x) = 0 otherwise. Determine whether f(x) dx = lim m. [ f(t) X-+0+ f(t)dt. 2. Show that -In(1-x) <₁ for x < 1.
1. Let f(1/n) = n for positive integers n and f(x) = 0 otherwise. Determine whether f(x) dx = lim m. [ f(t) X-+0+ f(t)dt. 2. Show that -In(1-x) <₁ for x < 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Let f(1/n) = n for positive integers n and f(x) = 0 otherwise. Determine whether
f(x) dx = lim m. [ f(t)
X-+0+
f(t)dt.
2. Show that -In(1-x) <₁ for x < 1.
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